It is well-known that sparse representations have a number of theoretical and practical advantages in computer vision and machine learning [1]}, [2]}, [3]}. In particular, sparse coding techniques have led to promising results in image classification, e.g. face recognition and digit classification. Sparse coding, as a generative model, is a very important way to extract the sparse representations. However, sparse coding has the expensive inference algorithm and does not use the label of the training data. Although some researchers use the supervised signals to learn compact and discriminative dictionaries [4]}, [5]}, [6]}, the expensive inference algorithm is still a problem. Since it is to train the dictionaries by using the labels, do we directly learn the discriminative dictionaries for avoiding the expensive inference?
